What is the critical region cut-off score for a two-tailed z test at alpha 0.05?

What is the critical region cut-off score for a two-tailed z test at alpha 0.05?

• A. -1.96
• B. 2.58
• C. 0.96
• D. 1.96

Answer: (D)

The test splits the alpha level equally in both tails, so 0.025 in each tail. Find the z value where the upper tail area is 0.025; that value is 1.96. So the rejection region is z ≤ -1.96 or z ≥ 1.96. The positive cut-off used to define the critical region is 1.96 (the negative cut-off is -1.96). The other numbers correspond to different alpha levels (2.58 for alpha 0.01) or are not standard cut-offs, so 1.96 is the correct threshold here. If you use the test statistic, you compare |z| to 1.96, and reject when |z| > 1.96.

The test splits the alpha level equally in both tails, so 0.025 in each tail. Find the z value where the upper tail area is 0.025; that value is 1.96. So the rejection region is z ≤ -1.96 or z ≥ 1.96. The positive cut-off used to define the critical region is 1.96 (the negative cut-off is -1.96). The other numbers correspond to different alpha levels (2.58 for alpha 0.01) or are not standard cut-offs, so 1.96 is the correct threshold here. If you use the test statistic, you compare |z| to 1.96, and reject when |z| > 1.96.